Hello guys, I've been trying to solve this problem all night and was wondering if I could get some help.

1. Suppose A is nxn nonsingular. Prove Det(A^-1) = 1 / Det(A)

I was trying to use the formula A^-1 = 1 / det(A) * adj(A) but had no luck

2. A = | 1/2 -1/2 | find A^-1

| 1/2x 1/2x|

I keep getting

1 1/x

-1 x